2.14AnalysisandDesignofFeedbackControlSystems State ...

Analysis and Design of Feedback Control SystemsState-Space Representation of LTI SystemsDerek RowellOctober 20021 IntroductionThe classical control theory and methods (such as root locus) that we have been using inclass to date are based on a simple input-output description of the plant, usually expressedas a transfer function. These methods do not use any knowledge of the interior structure ofthe plant, and limit us to single-input single-output (SISO) systems, and as we have seenallows only limited control of the closed-loop behavior when feedback control is control theory solves many of the limitations by using a much richer descriptionof the plant dynamics. The so-called State -space description provide the dynamics as a setof coupled first-order differential equations in a set of internal variables known asstatevariables, together with a set of algebraic equations that combine the State variables intophysical output Definition of system StateThe concept of thestateof a dynamic system refers to a minimum set of variables, knownasstatevariables.

The system shown in Fig. 1 has two inputs u1(t)andu2(t), and four output vari-ables y1(t),...,y4(t). If the system is state-determined, knowledge of its state variables ... of integrator blocks. A system of order nhas nintegrators in its block diagram. The derivatives of the state variables are the inputs to the integrator blocks, and each state

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